Question

Tick (✓) the correct answer:
The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm then the perimeter of the rectangle is
(a) 56 cm
(b) 60 cm
(c) 70 cm
(d) 80 cm

Answer 1

(c) 70 cm

$$\begin{gathered} \mathrm{Let}ABCD\mathrm{be}\mathrm{a}\mathrm{rectangle}\mathrm{and}\mathrm{let}\mathrm{the}\mathrm{diagonal}ACbe25\mathrm{cm},\mathrm{length}ABbe4x\mathrm{cm}\mathrm{and}\mathrm{breadth}BCbe3x\mathrm{cm}. \\ \mathrm{Each}\mathrm{angle}\mathrm{of}\mathrm{a}\mathrm{rectangle}\mathrm{is}\mathrm{a}\mathrm{right}\mathrm{angle}. \\ \therefore \angle ABC=90° \\ \mathrm{From}\mathrm{the}\mathrm{right}∆ABC: \\ A{C}^2=A{B}^2+B{C}^2 \\ \Rightarrow {\left(25\right)}^2={\left(4x\right)}^2+{\left(3x\right)}^2 \\ \Rightarrow 625=16x^2+9x^2 \\ \Rightarrow 625=25x^2 \end{gathered}$$

$$\begin{gathered} x^2=\frac{625}{25}=25 \\ \Rightarrow x=5 \\ \therefore L\mathrm{ength}=4\times 5=20\mathrm{cm} \\ \mathrm{Breadth}=3\times 5=15\mathrm{cm} \end{gathered}$$

∴ Perimeter of the rectangle = 2(20+15) cm
$=70cm$